I've got tons of milk jugs! I imagine you could use this idea and add a strap type of handle. Reusable gift bag if you did that. Change up what you cover it with for the purpose, Christmas fabric, Valentines Fabrics, etc.
fabric covered plain old cardboard boxes - SO CUTE! spray adhesive, and add grommets and rope handles. PLUS- a million links to other organizing ideas at end of this post! IHeart Organizing: Project Pretty: DIY Fabric Boxes & a Link Party!
Round Nesting Storage Baskets to Sew - Free Tutorial